I have seen this film several times, and watched it today (on TCM) solely because of Geraldine Fitzgerald. She is a much underrated actress and I have to admit I have had a crush on her since I first saw her (probably in "Wuthering Heights" 40 or more years ago). The real star in this movie, however, is Paul Lukas, and he deserved all the accolades he got. He makes it clear, whether we like it or not, that the end justifies the means. Naziism had to be stopped, and anything that helped do it was good. He gave his children a line about being bad, and that they should not be bad, but as he said earlier when conversing with adults, he would do this sort of thing again without hesitation. Lukas did give an excellent portrayal of a man caught in this situation, and made it clear that what he did was a very hard thing to do.
Some people think his victim was a Nazi, but I don't think so - I think he was only after the money. His Nazi associates knew this and that is why they did not have much use for him.
One interesting point in the film, and presumably also in the play, is the fact that Muller (Lucas) is a German. While the anti German hysteria of WWI was not repeated in WWII, there was considerable anti-German sentiment and some Germans were interred similar to what happened in California with people of Japanese ancestry. It was something of an act of bravery for Hellman to write a play about good Germans at this time (maybe she thought they were the ones who signed the Nazi-Soviet pact!). After all, the US and British air forces were bombing German cities and having no qualms about killing innocent civilians. I think, however, that the Dresden bombing and firestorm happened later, after "Watch on the Rhine" was released.
The title is something of a play on words, as the "watch" is looking west, from Germany. In fact, Watch am Rhein was a German army marching song - used in WWII, but the Nazis had their own marching song that was used as well. But Muller IS a German and he is engaged in his own "Wach am Rhein".
All the other actors did an excellent job here; although Bodo was too much there are children like him. I am surprised he did not give his father's secret away. In real life, he may very well have done so.